S1

Electronic Supplementary Information

Concentration Dependence of Dynamics for Microgel Suspension

Investigated by Dynamic Light Scattering Takuma Kureha,a Haruka Minato,b Daisuke Suzukib,c

Kenji Urayama,d and Mitsuhiro Shibayamaa*

aInstitute for Solid State Physics, The University of Tokyo, Kashiwa 277-8581, Japan. bGraduate School of Textile Science & Technology, Shinshu University, Ueda 386-8567, Japan. cDivision of Smart Textile, Institute for Fiber Engineering, Interdisciplinary Cluster for Cutting Edge Research, Shinshu University, Ueda 386-8567, Japan dDepartment of Macromolecular Science and Engineering, Kyoto Institute of Technology, Sakyo-ku, Kyoto 606-8585, Japan.

Figure S1. The intensity correlation function, 𝑔"

($)(𝜏) − 1, of the microgel suspension in the dilute and the intermediate concentration regions. The solid lines are the fitting curves using the single exponential function, Eq.(2), for C = 0.001 and 0.01 g ml-1 and the single and stretched exponential functions, Eq.(6), for C = 0.02-0.12 g ml-1 as described in the manuscript.

Electronic Supplementary Material (ESI) for Soft Matter.This journal is © The Royal Society of Chemistry 2019

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Figure S2. The measurement time dependence of the scattered intensity at 30 different positions. The values of the ensemble-average scattered intensity (<I>E) were also shown at each concentration. Note that the displayed data were cut from 600 s to 10 s of measurement time to make the data more visible. The range of scattered intensity on the vertical axis is different for each concentration because of the difference in incident light intensity.

1000

800

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0

Inte

nsity

/ kH

z

1086420Time / s

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0

Inte

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/ kH

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1086420Time / s

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1086420Time / s

<I>E = 438 kHz

0.001 g ml-1

<I>E = 621 kHz

0.01 g ml-1

<I>E = 659 kHz

0.018 g ml-1

<I>E = 421 kHz

C* = 0.02 g ml-1

2500

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/ kH

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1086420Time / s

<I>E = 396 kHz

0.04 g ml-1

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Inte

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/ kH

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1086420Time / s

<I>E = 298 kHz

0.08 g ml-1

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1086420Time / s

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1086420Time / s

<I>E = 287 kHz

0.12 g ml-1

0.14 g ml-1

<I>E = 291 kHz 1000

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0

Inte

nsity

/ kH

z

1086420Time / s

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1086420Time / s

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0

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nsity

/ kH

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108642Time / s

<I>E = 198 kHz

0.16 g ml-1

<I>E = 153 kHz

0.18 g ml-1

<I>E = 109 kHz

0.20 g ml-1

3000

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0

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nsity

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1086420

Time / s

<I>E = 357 kHz

0.10 g ml-1

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Figure S3. The cooperative diffusion coefficient (DFast) as a function of the effective volume fraction (φeff).

The values of DFast are obtained from region II and III.

Table S1. Summary of the results of the SLS measurements.

These parameters were obtained by fitting Eq.8. In the regions I (0.01 g ml-1) and II (0.02 and 0.04 g ml-1),

the SLS profiles exhibited the loose curves because the spherical shape existed in the suspensions as shown

in Figure 7. The obtained parameters were not significantly changed when C was increased from the region

I to region II. It suggested that the microgels were diffusive.

C R Rg σsurf

g ml-1 nm0.01 68 41 310.02 73 44 300.04 81 49 27

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Figure S4. The intensity correlation function, 𝑔"

($)(𝜏) − 1, of the microgel suspension measured at different scattering angles (θ = 30, 45, 60, 90, 120 and 140°). Each measurement time was 600 s at 25±0.3 °C.

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Figure S5. The decay time normalized by scattering vector (τq2) dependence of the intensity correlation function, 𝑔"

($)(𝜏) − 1, of the microgel suspension measured at different scattering angles (θ = 30, 45, 60, 90, 120 and 140°).

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Figure S6. The intensity correlation function, 𝑔"

($)(𝜏) − 1, of the microgel suspension at 30 different positions.

Figure S7. Dynamic component, 𝑔*,,

(-)(𝜏) , in the ensemble-average field correlation function,𝑔*

(-)(𝜏), at C = 0.20 g ml-1. The black solid and blue dotted lines are the fitting curves using Eq.(12) and Eq.(6), respectively. The best fit was obtained using Eq.(12), which is the double stretched exponential functions.

0.01

2

46

0.1

2

46

1g2 (τ

)-1

10-3 10-2 10-1 100 101 102

τ / ms

0.01

2

46

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2

46

1

g2 (τ)-1

10-3 10-2 10-1 100 101 102

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0.01

2

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g2 (τ)-1

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0.01

2

46

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2

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g2 (τ)-1

10-3 10-2 10-1 100 101 102

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0.01

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1g2 (τ

)-1

10-3 10-2 10-1 100 101 102

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2

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1

g2 (τ)-1

10-3 10-1 101 103

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0.01

2

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2

46

1

g2 (τ)-1

10-3 10-2 10-1 100 101 102

τ / ms

0.01

2

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1

g2 (τ)-1

10-3 10-1 101 103

τ / ms

0.01

2

46

0.1

2

46

1

g2 (τ)-1

10-3 10-1 101 103

τ / ms

0.01

2

46

0.1

2

46

1

g2 (τ)-1

10-3 10-1 101 103

τ / ms

0.01

2

46

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2

46

1g2 (τ

)-1

10-3 10-1 101 103

τ / ms

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46

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2

46

1

g2 (τ)-1

10-3 10-1 101 103

τ / ms

0.001 g ml-1 0.01 g ml-1 C* = 0.02 g ml-1

0.01

2

46

0.1

2

46

1

g2 (τ)-1

10-3 10-2 10-1 100 101 102

τ / ms

0.025 g ml-1

0.03 g ml-1 0.04 g ml-1 0.08 g ml-1 0.10 g ml-1 0.12 g ml-1

0.14 g ml-1 0.16 g ml-1 0.18 g ml-1 0.20 g ml-1

0.015 g ml-1